プレプリどんどん: math.NT

arXiv math.NTの新着論文15本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-10/

1. Refuting a Conjecture of Umans and Wang on Arithmetic-Progression Divisor Covers
2. Squarefree numbers in short intervals: explicit and formalized
3. Anticyclotomic Iwasawa theory of CM elliptic curves at ramified primes
4. A Combinatorial Approach to Vorono{\"i} Theory
5. An extension of Ramanujan-Guinand identity for the Dedekind zeta function and a new formula for $\zeta_\mathbb{F}(2)$ and $\zeta_\mathbb{F}(2m+1)$
6. On semi-stable integral models for Shimura varieties
7. Modularity of Higher Theta Series III: Proof of the Modularity Conjecture
8. Towards the Fontaine--Mazur conjecture for GL(2)
9. Heath-Brown identities for fractional powers of $\zeta$
10. On the Existence of Primitive Polynomials $f(x)=g(x)+ \lambda$ over Finite Fields
11. Siegel zeros and small gaps between zeros of the Riemann zeta function
12. $\Delta$-separated Sidon sets in additive number theory
13. Universality for Random $p$-adic Polynomials and Random Matrices Via the Resultant Distribution Method
14. A three-dimensional corner configuration involving the Omega function
15. Arithmetic Properties of Mixed Stirling Numbers of the second kind

arXiv math.NTの新着論文19本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-07/

1. Rigidity of Averages over the Two Largest Prime Factors
2. Explicit Algebraic Numbers all whose Integer Parts of Powers are Composite
3. The sesquicentennial of the prime number $2^{127} - 1$
4. Trianguline representations and locally analytic principal series of ${\rm GL}_2({\mathbb Q}_p)$
5. Asymptotic uncorrelations between functions with squarefull kernel and functions of invariant average
6. Modularity of Point Counts for the Curves $X^a=Y^b$: New Rogers--Ramanujan Identities
7. Iwasawa invariants and exceptional pairs of certain abelian fields
8. Generalised Gauss--Kuzmin Distribution for Klein sails in $\mathbb R^3$
9. Hearing Tamagawa Factors modulo $q - 1$
10. Hybrid Weyl Subconvexity over Imaginary Quadratic Fields
11. Bounds for moments of twisted quadratic characters of prime modulus
12. Periods of E-operators
13. Strong Weil Degree Divisibility at Higher Levels
14. Average analytic rank for the $L$-functions of the elliptic curves $y^2=x^3-dx$
15. The good reduction of generalized Kummer surfaces in the non-supersingular case
16. On the motivic cohomology of some singular rings
17. New central $q$-binomial identities
18. Higher-Order Cyclotomic Congruences for $q$-Secant and Generalized $q$-Euler Numbers
19. Exact renewal laws for minimal common-denominator profiles in simultaneous Laurent-series approximation

arXiv math.NTの新着論文16本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-06/

1. Rational spanning sets of level-one cusp forms from Eisenstein series at prime levels
2. The distribution and the structure of the maximum of partial sums in families of trace functions
3. The $5$-divisible integer group determinants for the elementary abelian group of order 25
4. On the Burgess bound and Pythagorean triples involving primitive roots
5. Powers as Fibonacci Sums
6. Regularized Multitangent Functions and Reduction Theorem
7. Construction Of Non-Odd Galois Representations With Large Image
8. On the $L^2$ restriction norm of large level
9. A proof of the Freiman-Lev conjecture
10. Adelic framed form class groups and explicit class field theory
11. Quantitative Khintchine on the parabola with non-monotonic approximation functions
12. Chebotarev geodesic theorem: non-split case
13. An Integral Mean Value Theorem for Weyl Sums over Broken Arcs
14. Weyl Subconvexity for $\mathrm{GL}_2$ with Simple Supercuspidal Ramification
15. Dualizable Additive Categories
16. Sparse Random Covers and Growth of Torsion in First Homology

arXiv math.NTの新着論文16本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-05/

1. A Classification of Multiply Monogenic Quartic Orders
2. Counting in Vieta graphs over $\mathbb{F}_p$
3. On pairs of primes with small order reciprocity
4. Admissible Pairs: A Variation to Pollock Conjectures
5. Mellin Transform Formulas for Anderson Modules and Hints of Modularity
6. Erd\H{o}s-Moser Equation in Arithmetic Progressions
7. Explicit Jordan decompositions for ideal lattices in CM fields
8. No three algebraic conjugates of degree sixteen sum to zero
9. An upper bound for counting algebraic tori over $\mathbb{Q}$ by Artin conductor
10. On the distribution of $\phi(\psi(n))$ and $\psi(\psi(n))$
11. Non-split Cartan curves and a characterization of fake elliptic curves
12. On Diophantine equations over the integer rings of quadratic fields
13. The extended Fargues--Scholze spectral action
14. Murphy's law in non-abelian Hodge theory
15. Strichartz estimates for quasi-periodic functions on long time intervals: An arithmetic approach
16. Refined upper bounds on Schur-like numbers

arXiv math.NTの新着論文54本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-04/

1. Random Multiplicative Functions with Periodic Weights
2. Ljunggren--Jacobsthal and Bailey-Type Congruences for Rectangular Gaussian Binomial Coefficients
3. Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields
4. Positive rational series for reciprocal powers of Catalan's constant and Dirichlet beta values
5. Negative bias in moments of the Legendre family of elliptic curves
6. Machine learning the arithmetic of Boyd's Mahler measure conjectures
7. Faster Deterministic Integer Root Finding for Integer Polynomials
8. Dynamical Canonical Heights and Finite Trees
9. The Minimal Degree of Salem Numbers with Negative Trace
10. Cycles for Rankin-Selberg $L$-functions, I: automorphic periods
11. de Rham theory and locally analytic vectors
12. Arithmetic of elliptic curves induced by regular Diophantine triples
13. Lattice point sumsets and asymptotic approximate groups
14. Weights in \'etale cohomology over mixed-characteristic local fields and applications to anabelian geometry
15. Bilinear Kloosterman sums over small boxes and uniformity of a random walk
16. Distribution of simplices in the discrete and continuous settings
17. On binomial order and primitivity of irreducible quadratic polynomials over finite fields
18. Murmurations of quadratic and cubic characters over function fields
19. Weighted averages of Bernoulli polynomials and the Gamma function over regular integers modulo $n$
20. Families preserving isomorphisms via techniques in anabelian geometry: with an application to a generalized Neukirch-Uchida theorem
21. Nine-distance theorem and growth of best-approximation denominators
22. A Coates-Sinnott-type Theorem for First Derivatives of Artin $L$-Functions
23. Bounds for Mertens Sums
24. Algorithmic universal \'etale $(\varphi,\Gamma)$-modules
25. On the Petersson norm $\langle\theta_{\psi},\theta_{\psi}\rangle$
26. Constructing Self-Regulating Field Theoriesfrom Primal Wave Fields without Background Manifolds:The Emergence of the Coordinate Continuum
27. A New Characteristic-Uniform Model for Elliptic Curves -- Theory, Arithmetic, and Applications
28. Factorial residues modulo a prime: beyond the square-root bound
29. Integral Representations and Asymptotics for a Family of Areal Mahler Measures
30. The Local Four-Square Problem over \(\mathbb{Z}_{p^k}\)
31. Every quasiperfect number has at least eight distinct prime factors
32. Multiple Zeta Values
33. On the $L^6$-norm of holomorphic Hecke eigenforms
34. Mahler measures at interior CM points: proofs of two conjectures of Samart
35. Samart's conjecture n_4(81)=40M_7: the exact CM evaluation and the two obstructions. A status report
36. An intermediate conjecture between Goldbach and Dubner: every even number is the sum of a prime and a twin prime
37. Isogeny graphs of elliptic curves in characteristic zero
38. Automorphic functions for square-zero extensions of curves over finite fields
39. Additive decompositions of multiplicative subgroups in prime fields: a self-contained approach
40. Associated graded modules for modular representations of quaternion algebras
41. Identities involving the number of missing integers in partitions - combinatorial proofs
42. Localization and elliptic motivic relations
43. Fixed Perimeter Analogues of Several Partition Results Related to Parity
44. Arithmetic hypergeometric $\mathcal {D}$-modules and exponential sums on reductive groups
45. The finitude of the fibers of the complementary Bell numbers
46. Collinear Interior Lattice Points in Triangles Satisfying $B(T)\in\{4,5\}$
47. Convolutive sequences, II: Parametrizations
48. Schur--Plucker Geometry of the MDS Locus for Principal-Ideal Codes
49. Square-Difference-Free Sets beyond the Three-Quarter Barrier
50. Intertwining Operators for Siegel Parabolics over Finite Fields
51. The catenary degree of monoids of product-one sequences
52. Square-integrability of holomorphic differential forms on locally symmetric varieties
53. Counterexamples to the Minimum Period Conjecture for Restricted Partition Functions
54. Comparing local-global obstructions on algebraic stacks

arXiv math.NTの新着論文10本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-03/

1. Multiplicative dependence in the sumset of multiplicative groups
2. The Fine-Structure Hierarchy of Prime Biases and the Universal Dominance of $-1 \pmod N$
3. Small points in radical extensions of number fields
4. Generalized Wieferich primes and monogenic trinomials
5. An Introduction to p-adic Hodge Theory
6. A sharp almost sure upper bound for partial sums of random multiplicative functions
7. On the size of $h$-fold sumsets
8. The least quadratic residue and integers represented by quadratic forms
9. On Generalized Chebyshev polynomials
10. Slice and Partition Rank Criteria for Polynomial Zero-Avoidance

arXiv math.NTの新着論文23本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-31/

1. The exceptional set of the Goldbach problem
2. Multivariate counting of wild abelian extensions
3. On some Diophantine and Ergodic properties of the Schneider map over function fields
4. On the greatest common divisor of $n, \lfloor \alpha_1n\rfloor, \lfloor \alpha_2n^2\rfloor, ..., \lfloor \alpha_kn^k\rfloor$
5. An Asymptotic Bound for Non-covering Congruence Systems over Fq[x]
6. Perfect $2$-codes over arbitrary alphabets
7. Schur Eisenstein series and Schur MacMahon series
8. Irrationality of finite logarithms in a congruence-class ad\`ele ring
9. On a question of Gowers related to Littlewood's conjecture
10. On the Gow--McGuire Conjecture for Primitive Quadratic Polynomials
11. Random linear configurations in dense sets and primes
12. Regularity of Diophantine quadruples over $\mathbb{Q}(i)[X]$
13. Euler-type Recurrence Relations for Partition Functions with Congruence Conditions
14. Eventually greedy best Egyptian underapproximations of rational numbers via optimal control
15. Ginzburg's conjecture on the unramified computation of Eulerian integrals
16. Vertex volumes, lattice-minima tails, and height zeta functions for the standard arithmetic quotient of $\operatorname{PGL}_d$
17. Deformation of the absolute Galois groups of number fields
18. Schwartz spaces on L-monoids: non-Archimedean
19. Sumsets and generalized arithmetic progressions in multiplicative subgroups
20. $\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns
21. Proof of a Conjectured Ramanujan Type Master Theorem for Powers of the Cosecant
22. Types and collapse for cuspidal representations of groups acting on trees
23. Franklin's identity for $n$-color partitions and companion Beck-type identities

arXiv math.NTの新着論文18本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-30/

1. On purity of Anderson t-modules
2. Inclusions between p-bounded crystalline loci in dimension two
3. Bhargava Gamma functions for determinant-admissible sets
4. On the transcendence of twisted special $L$-values at non-negative integers in characteristic $p$
5. Improved Bounds for Distinct Multiples in Intervals
6. On Oliver's relations between infinite series and infinite products
7. On a Question of Lehmer concerning the Comtet Numbers
8. On the higher algebraic $K$-groups of arithmetically equivalent number fields
9. Explicit mock Heegner points and BSD formula on certain Mordell curves
10. Dimensions of Orbit Closures and Discrepancy for Dynamical $p$-adic Sequences
11. Kuroda's Class Number Formula
12. On a problem of minimal additive complements for not eventually periodic $S$-difference sets
13. On the second moment and non-vanishing of central values of Hecke $L$-functions of $r$-th order characters
14. Formally certifying number field invariants
15. Fuglede's Conjecture on Cyclic Groups of Square-Free Order: The Case of Rapidly Growing Prime Factors
16. Asymptotics of the spectral determinant of the weighted Laplacian for a sequence of compact Riemann surfaces of infinitely growing volume
17. Splitting Brauer classes by genus one curves over number fields
18. A topological interpretation of numbers

arXiv math.NTの新着論文23本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-29/

1. Extremal Chowla sets and their linear analogues: A human-AI mathematical investigation using Co-Scientist
2. Transcendence of multivariate Mahler functions and algebraic relations between their values
3. Twisted automorphic descent to odd GSpin groups and applications
4. On certain $D(9)$ and $D(64)$ Diophantine triples
5. The Explicit Hypergeometric Modularity Method III
6. Diagonal cycles on Shtukas and the adjoint $L$-function
7. On the Vanishing of the Brauer-Manin Obstruction for Normic Bundles
8. Beyond endoscopy for the symmetric square representation: The simple trace formula case
9. Extreme values of quadratic Dirichlet $L$-functions with prime-related moduli
10. On an asymmetric additive energy inequality
11. Hypernatural numbers in arithmetic Ramsey theory
12. Refined Humbert Invariants in Supersingular Isogeny Degree Analysis
13. An Asymptotic Formula in Waring's Problem for Seventeen Fourth Powers with Almost Equal Summands
14. Multiplicative subgroups are not restricted sumsets
15. Intersection Cohomology of Igusa Stacks
16. $d$-Translated Unit Sensitive Primes
17. Collision of Orbits for Families of Polynomials Defined over Number Fields
18. Local Moments of M\"obius Fourier Polynomials and the Riemann Hypothesis
19. A Criterion for Equidistribution along the $\Omega$ Function over Polynomial Sequences with Applications
20. Graph integrals, Feynman periods, and single-valued multiple zeta values
21. Kernel-Checked Exclusions for the Erd\H{o}s-Selfridge Odd Covering Problem: Any Odd Covering of $\mathbb{Z}$ Has lcm Exceeding 10000
22. Solution of Erd\H{o}s problem $\# 443$
23. Iterate Wronskians over $\mathbb{R}^d$ as $N$-ary brackets on $\mathbb{R}[x^1,\ldots,x^d]$: the $N$-bonacci numbers bound the highest total degrees

arXiv math.NTの新着論文31本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-28/

1. Jittered sampling and probability measures
2. Tadpole Nahm sum as a Wronskian
3. Unshared zeros of Dirichlet $L$-functions
4. On the Frobenius Number of Quotients of Numerical Semigroups
5. Finite length for unramified $\mathrm{GL}_2$: beyond multiplicity one, non-semisimple case
6. On the role of higher roots in prime ideal races
7. Explicit Twisted Hilbert Class Components Beyond Classical Irregularity
8. On the Comparison of the D-new Modular Degree and the Shimura Degree of Modular Abelian Varieties
9. Modularity of Nahm Sums Dual to Zagier's Rank-Three Examples
10. A lower bound for the distance between CM points on Shimura curves
11. Matrix Kloosterman sums and product-trace estimates for semisimple algebras
12. On the automorphisms of numerical power monoids
13. Optimality of Wouter van Doorn's Upper Bound for the Mayer-Erd\H{o}s Farey Problem
14. Self-Referential Leading Digits of Exponential Sequences: Arithmetic Structure and Certified Search
15. Algebraic values of transcendental power series with geometric coefficient moduli
16. Larger sieve with height function and uniform bounds for integral points on curves over number fields
17. Slowly Divergent Trajectories for Weighted Singular Vectors in R^2
18. Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves
19. Signs of Square-Free Fourier Coefficients of Half-Integral weight cusp forms and the Congruent Number Problem
20. Bilinear forms with Kloosterman sums via quadratic characters
21. On $C^k$-functions mapping $\mathbb{Q}$ into itself and Mahler's problem on Liouville numbers
22. A Salem-Spencer-Type Construction for Large Subsets of Integer Grids with No Isosceles Right Triangles
23. Non-isomorphism of rings of integer-coefficient holomorphic functions on disks of varying radius
24. Tiling a triangle into a prime number of congruent triangles
25. Additive Bases from Primitive Dyck Words: Regular Underapproximations, Motzkin Coding, and Digit Lifting
26. On the Thickness of Infinite Generalized Sidon Sets, II
27. Beyond the Adams Conjecture
28. Cyclic codes and cyclically covering subspaces
29. Multiplicative irreducibility of shifted multiplicative subgroups in the extremal case
30. Simply branched covers of curves and wild conductor exponents
31. On the problem of large gcd for disjoint residue classes